Topics - Bill S

Consider Einstein’s thought experiment in which he imagines himself travelling at a speed that is approaching that of light, holding a mirror in front of his face. If, as was believed at the time, light travelled at about 300,000kps relative to the aether, then, as Einstein and his mirror reached the speed of light, the light trying to leave his face would not do so, and would therefore not reach the mirror, so would not be reflected back. In this thought experiment, as Einstein reached light speed his reflection vanished from the mirror. Einstein reasoned that this ran contrary to Galileo’s concept of relativity. According to which, someone travelling at a constant velocity, without reference to any object outside his or her frame of reference, should not be able to distinguish between being in motion and being stationary. If one were not able to see one’s reflection in the mirror, in which the reflection was visible when stationary, then one would have an experiment to distinguish between being stationary and being in motion.

Recast Einstein’s thought experiment in terms of Galileo’s below-deck scenario: a sailor would know if the ship were moving at the speed of light because his reflection would vanish. In Galileo’s scenario all the insects etc. move within the moving cabin exactly as they did in the stationary cabin because the entire system is moving in unison. If one shone a light across the cabin its speed would be measured as 300,000 kps, whether the ship was moving or not.

Prior to Einstein’s discoveries it would have been assumed that this was because the speed of the ship was being added to, or subtracted from the speed of light, as would be the case with the various creatures in Galileo’s scenario. Until Einstein came to the conclusions that arose out of his thought experiment it would have been reasonable for him to assume that the speed of the light leaving his face would have been measured as 300,000 kps, plus his speed through the aether. Thus, why would he have concluded that his reflection would vanish from the mirror when he travelled at light speed?

Until he made his later discoveries, would he have had any reason to assume that the light travelling from his face to the mirror would have been measured as anything other than almost 600,000 kps by an observer outside his RF? Unless, of course, Einstein’s motion through the aether caused an aether wind which effectively reduced the light’s speed between Einstein and the mirror to zero as he reached light speed. To avoid this, Einstein and his mirror would have to be completely shielded from the aether, apart from a small portion which they carried with them in their RF, in order to equate this thought experiment with that of Galileo and his below-deck goings on.

It seems as though it would have been necessary to have been in possession of the conclusions drawn from Einstein’s thought experiment in order to have been able to formulate and analyse it.

A frequently found example of the process of increasing entropy involves a closed box containing a quantity of O2 molecules. At the start, they are bunched together. With time, they spread out to fill the space. It is argued that there are many more ways of achieving the second configuration than the first, therefore entropy has increased.

Intuitively, that seems fine; but let’s look more closely. Are all the O2 molecules identical? If they are, what difference might that make?

Consider a box containing three identical molecules. Call them A, B and C. We will have positions x, y and z. This would seem to give us three possible combinations,

1) A - x, B - y, C – z 2) A – y, B – z, C - x 3) A – z, B – x, C – y

but, if the molecules are indistinguishable, how, for example, does configuration 1 differ from 3?

If one cannot distinguish between A, B and C; aren’t all three configurations identical?

John Gribbin says, regarding the tachyon: “So if a tachyon were created in some violent event in space, it would radiate energy away furiously…..and go faster and faster, until it had zero energy ……and was travelling at infinite speed”.

“Infinite speed” is a term that trips easily off the tongue, but is not easy to define. If it means anything, surely, it must mean that a journey from A to be B would take no time. In other words, one would be at A and B simultaneously.

If A and B are physically separated, then a situation arises in which an instantaneous response occurs in separated locations. Relativity must forbid this.

This is the best (simple) explanation I’ve found, but I ran into a problem with:“Descartes discovered that with this framework he could link geometric shapes and equations. Thus, a circle with a radius of 1 can be described by the equation x2 + y2 =1.”

This seemed to say: x=1, so x2 =1; y=1, so y2 =1. Therefore, 1+1=2, but the circle has radius 1.

Please forgive the ponderous nature of this post; it has to do with my thought processes.

Consider entropy as a measure of disorder. In general, we tend to think of disorder as increasing as things spread out. The ubiquitous example of the cup (compact, ordered, low entropy) being smashed and thus, becoming fragments (spread out, disordered, higher entropy) comes immediately to mind. However, is this always the case?

Consider next a cloud of dust in space. This might be spread out and seemingly disordered, but because its particles have mass they will gravitationally attract one another. Thus, as they clump together, they become less spread out and, intuitively, more ordered. Does this mean that gravity can reverse the normal pattern of progress from low to high entropy?

Entropy is defined as the logarithm of the number of microstates accessible to a system. Could it be that under the influence of gravity, a system has more microstates when it has collapsed than it had before?

The answer would seem to be “yes”. For example: A black hole, which is created out of a large amount of matter that has been condensed under gravity into a very small area, has, we are assured, a huge entropy; far greater than the entropy of the total matter in its non-compacted state. This must mean that the available number of microstates increases as the matter becomes more compressed.

An interesting experiment; worth reading; but wouldn't one have to make the assumption that the "arrow of time" was actually governed by the 2nd law in order to claim to have reversed time?

Then there is this.

Quote

“It’s not that it’s contradicting any laws of physics,” says Vlatko Vedral, a physicist at the University of Oxford not involved with the study. The standard second law of thermodynamics assumes that there are no such correlations. When the second law is generalized to take correlations into account, the law holds firm. As the heat flows, the correlations between the two nuclei dissipate, a process that compensates for the entropy decrease due to the reverse heat flow.

What follows may have an ominous look of familiarity about it, but please be patient. As I said in another thread, it is a last attempt to get my ideas straight.

Acknowledging that any necessary modification or explanation can come later; could I ask to start with yes/no answers to a couple of questions? I’ll set a good example by giving my own answers, and, of course, being prepared to defend them later.

1. In our perceived 4+1 dimensional Universe, is it possible to formulate a “working” concept of infinity/eternity beyond a mathematical infinity? Yes.

2. Given that there is something, can there ever have been (absolutely) nothing? No.

There have been suggestions that the Higgs field could have been the inflation. I’ve not kept up with developments (if there have been any) relating to this idea, but a few thoughts come to mind, and invite comments.

1. If the Higgs field is linked to inflation it must have been "created" in the first instant of the Big Bang.

2. If the Higgs field is the inflation it must have preceded the start of inflation.

3 If it is not the inflation it could have emerged after inflation started; in which case, could it have been the influence that "stopped" inflation?

Considering the progress since the first direct observation of gravitational waves, it seems likely that, In the not-to-distant future, it may be possible to identify the galaxy in which the waves originate.

Popular science literature often raises questions about a “boundary condition” at the Big Bang, which necessitated a low entropy scenario.

In the FLRW model the Universe in its first instant is miniscule (a single quantum, as Lemaître described it). This “Primordial Atom” contained all the matter and energy of the Universe, which completely filled the tiny space it occupied. In that first “quantum” matter/energy occupied all the available space; there was no room for “manoeuvre”; entropy could not have started evolving until more space became available (?).

What does it mean to equate this to a low entropy boundary condition? Surely, in that first instant, entropy was at the maximum possible for the conditions, albeit for only the briefest instant.

I suspect that this is a poor way to describe it, but it is what tends to come out of Pop Sci. Possibly I should be talking in terms of thermal equilibrium, restricted degrees of freedom and low/high entropy. However, the low entropy boundary condition is frequently met. A particular example is the writing of Sean Carroll.

Certainly, a common image is that of an expanding sphere, like an inflating balloon. This, of course, is not to be confused with the “balloon analogy” in which the Universe is represented by the two-dimensional surface, rather than by the whole balloon.

Let’s think briefly about this visualisation. Without in any way suggesting that the Universe actually has a physical boundary, the mental image will almost certainly have one. You, of course, will be at the centre of this sphere, and will see the rest of the Universe moving away from you. The most up to date figure for the expansion rate of the Universe is “67.3 kilometres per second per megaparsec”. (A megaparsec is defined as a distance equal to 3.26 million light years.)

Just to make the arithmetic easy, let’s say our imaginary sphere has a radius of one thousand megaparsecs. Obviously, this is much too small, but it is just a simple thought experiment. This means that the imaginary boundary will be separating from you at 67,300 kilometres per second. The galaxies are being carried along with the expanding space, so any celestial body that is within the last 67,300 km. on this side of the boundary now, will be outside the present boundary position in one second’s time. It will be in newly created space; space that was not there a second ago; at least, it will be if the expansion of the Universe really does involve the constant creation of new space. Think a little more about this, though. An observer, say, on a planet that has, from your perspective, just passed into the newly created space, will perceive himself as being at the centre of a spherical universe, and will think that you have just passed into newly created space.

This tells us a couple of things:

(1) If the Universe is homogeneous, and in order to do any meaningful cosmology we must assume it is, we cannot define a physical boundary.

(2) We cannot define any part of the Universe; rather than any other part; as being the newly created part. This must mean that every part of the Universe is expanding: new space is coming into existence everywhere in the Universe, all the time. No part is newer than any other part. Newness is relative!

How can it be demonstrated that an unobserved quon (sensu Herbert) takes every possible path from A to B?

One finds it stated that this is the case. I

The problem I have is that in order to know that a quon is at A, it must be observed. Surely, once it is detected it must be at a specific location, and from that point on, act as though it were a classical object, and follow a specific path.